Formulated by Einstein, the
two-black-hole problem holds extremely important
implications for astrophysics and cosmology.

Once upon a time, on a small planet in a galaxy called the
Milky Way, black holes were considered a fascinating
theoretical artifact from the mathematics of general
relativity  interesting concept, great stuff for
science fiction. We've come a long way since 1915 when
Einstein laid out his theory that rocked our world.

In 1969 American physicist John Wheeler coined the phrase
that gives resonance to the concept of points in space-time
where matter is so condensed, gravity so fiercely omnivorous,
that it swallows everything, including light, that gets too
close. Only 12 years ago, with observational evidence
beginning to trickle in  swirling gas and star
coalescence at the center of galaxies  Stephen Hawking
wrote, prophetically, in A Brief History of Time: "The number
of black holes may well be greater even than the number of
visible stars."

A jumble of blue star-clusters, glowing gas clouds and dust
lanes surround an apparent black hole at the center of galaxy Centaurus A,
a mere 10 million light years from Earth, recorded by the Hubble Space
Telescope.

Since 1994 the Hubble Space Telescope and, more
recently, NASA's
Chandra X-ray Observatory have convincingly lifted black
holes from theory into reality. With data from these eyes in
space, scientists have identified over 30 likely black holes
and counting. They come in a range of sizes, from
supermassive (like the monster with the mass of 30 million
suns at the center of the Andromeda galaxy) to many that are
small ( a few solar masses) and most recently a middleweight
(about 500 solar mass) in galaxy M82.

Still, even with Hubble and Chandra, the evidence is
circumstantial. Fundamentally, a black hole is invisible.
Looking for one, as Hawking said, is like trying to find a
black cat in a coal cellar. The observations offer reasoned
surmises about an undetectable agent lurking in the interior
of detectable phenomena. As Penn State astrophysicist Pablo
Laguna and post-doctoral fellow Deirdre Shoemaker like to
point out, the way to clinch, indisputably, that black holes
exist and that Einstein's equations are right is to detect
gravity waves from two black holes.

Tuning the Gravity-Wave Radio

Detecting gravity waves is the job, a big one, cut out for
LIGO, Virgo and GEO600. LIGO (Laser
Interferometer Gravitational-Wave Observatory) is two
NSF-funded gravity-wave detectors  in
Louisiana and
Hanford, Washington  now undergoing testing. Virgo and
GEO600 are under construction in Europe (near Pisa, Italy and
in Germany). Together these projects represent a pioneering
effort that scientists hope will lead the way to an
invaluable new set of eyes  gravity eyes  for
seeing the universe. But it won't be easy, especially since
no one ever has detected a gravity wave.

Along with anticipating black holes, Einstein's theory
predicts that accelerating movements of massive objects in
space, such as supernova explosions and black holes, will
produce ripples traveling at light-speed through space-time.
As with black holes, there's indirect evidence he was right,
but compared to other wave phenomena, like electromagnetism,
which brings us radio and TV, gravity waves are very weak.
Einstein speculated they might never be detected. If you
think of LIGO as the gigantic antenna for a radio receiver,
the strongest possible signal might be a faint crackle as you
turn the dial. To improve the chances of hearing the first
crackle of gravity from the cosmos, LIGO needs to know where
to set the dial to tune in two black holes colliding with
each other.

To do this, researchers like Laguna and Shoemaker are
using supercomputers, the most powerful they can find, to
numerically solve Einstein's equations. Their field is called
numerical relativity, and with collaborators at the
University of Texas and the University of Pittsburgh, Penn
State has assembled one of the leading groups in the world.
In recent work, relying on systems at PSC, at NCSA in
Illinois and elsewhere, this multi-university team
successfully simulated two black holes merging in what's
called a grazing collision  only the second time this
has been accomplished. Their numerical approach, called
black-hole excision, makes a notable dent in the
two-black-hole problem, the major challenge of this
challenging field.

"Einstein's equations describe gravity via an elegant but
complicated set of non-linear partial differential
equations," says Laguna. "Their complexity requires the most
powerful supercomputers available. Accurately solving the
two-black-hole problem, formulated conceptually by Einstein
80 years ago, will represent an historic moment in the
development of general relativity theory, with extremely
important implications for astrophysics and cosmology."

The mathematics of a single spherical black hole sitting
and spinning in space was worked out long ago by German
astronomer Karl Schwarzschild, who in 1917 from his deathbed
in effect discovered the black hole, without naming it, as
one of the implications of Einstein's theory. A single black
hole by itself, however, doesn't make gravity waves. Add
another black hole, the interesting and many believe very
relevant situation of two black holes merging with each other
 often called a binary black hole  and you
fiendishly complicate the mathematics, to the point where the
only hope is supercomputers.

"As in most physical studies," says Shoemaker, "you want
to look at the complicated and more realistic situations to
test what you know. With general relativity, you can't put
two of these compact objects together and get a solution
without advanced computational techniques. Two black holes
takes the theory into a dynamical regime, where you can make
predictions and then, if experiments verify the predictions,
you know how far the theory is correct."

It's a mutually beneficial relationship. To verify the
predictions, you need detectors. LIGO, Virgo and GEO600,
likewise, need predictions. Many believe that colliding black
holes is the best shot at detecting gravity waves. Theory
says it's one of the strongest signals on the gravity-wave
dial. To know if a crackle of static is the dance of two
black holes or cosmic noise, the detectors need the answers
numerical relativists are working to provide.

Black Holes without the Holes

"Abandon hope, all ye who enter here," said Dante of the
entrance to Hell. He might have said the same about the event
horizon of a black hole. In solving Einstein's equations,
Schwarzschild started with the idea of an infinitely
condensed mass and showed that space-time curves around it
and closes on itself. Once matter or light enters space-time
within a certain radius from that point  initially
called the Schwarzschild radius, now the event horizon 
there's no escape. The region inside the horizon is cut off
from events outside. This principle, called cosmic
censorship, underlies black-hole excision.

The killer for simulating black holes is the singularity,
the point of infinite density and space-time curvature that,
mathematically speaking, makes a black hole a black hole.
"The most crucial aspect of numerically evolving spacetimes
containing black holes," says Laguna, "is without doubt the
accurate and long-term handling of the singularities these
objects represent."

Simply put, the numbers get too big too fast, and the
computation crashes. "If you get too far inside the black
hole," says Shoemaker, "you run into huge gradients that kill
your calculations. There are basically two alternatives. In
one of them you exploit the relativity of time; in effect you
slow down how fast clocks tick near the black hole to avoid
approaching that area. The other way is to remove the
dangerous area. That's what we did."

The first approach, avoiding the singularity, has been
more popular, and a group at the Albert Einstein Institute
near Berlin has employed it with some success. It has the
drawback that to slow down time inevitably adds to the
already severe computational demands. With software they call
AGAVE, the Penn State-Pittsburgh-Texas team has taken the
less-traveled road of surgically removing the singularity
from the domain of the calculation. About two years ago, the
Pittsburgh group successfully excised the singularity for a
single black hole moving in space. AGAVE extends this
approach to colliding black holes, in effect, simulating two
black holes without the black holes.

How, you might ask, can you compute gravity waves from a
black hole if you eliminate the black hole? The secret, says
Laguna, is in the horizon. Cosmic censorship. Since
information about anything across that threshold is cut off,
physical processes outside the horizon aren't affected by
what happens inside. "As long as the spacetimes with and
without the singularities agree at the points where the cut
is made," says Laguna, "both situations should be equivalent
for an observer outside."

Much easier to say than implement, notes Shoemaker. The
numerical intricacies of cutting out the hole from the
grid-like domain of the computation and, at the same time,
keeping track of its movement in time, are daunting. Using
PSC's CRAY T3E, AGAVE underwent extensive development and
testing prior to the grazing collision simulation.

Grazing Collision of Two Black
Holes
In these two snapshots from the simulation, transparent
spheres represent the "apparent" horizon of the black holes. The first
snapshot shows two equal-mass black holes caught in each other's
gravitational pull; the second shows the large black hole formed as they
merge. The bluish area inside the spheres represents the excised region.
Color gradations (from red to purple) indicate relative strength of the
gravitational field.

The grazing collision is a milestone  compared to
the symmetry of a head-on crash, which has been done before
 because it adds a layer of complexity and realism.
With 40 processors of NCSA's SGI Origin 2000, it required
nearly 100 hours. There's simplifying assumptions, such as
two equal mass black holes, but the result is, you might say,
a smashing success that pushes beyond prior work.

Excision tamed the numerical instabilities of the
singularity long enough for the two black holes to merge
completely and evolve for a short period as one large black
hole before the simulation crashed. It's not the end of the
road by any means, stress Laguna and Shoemaker. There's not
yet accurate gravity-wave predictions to hand over to LIGO.
But the next mountain now looks more climbable. That
mountain, two black holes that orbit each other before they
coalesce, is a few years away say the researchers.

Further help is coming, notes Laguna, whose eyes light up
thinking of PSC's new terascale system, more than 2,700
powerful processors with a peak capability of over
six-trillion calculations per second, a leap forward that
will allow the team to push further with AGAVE. "We believe
one of the severe problems we have now is that the merged
black hole gets too close to the boundaries of the
computational domain. With the new machine, we can shift the
outer boundary outward."

Some day, not that far away, a crackle of static will come
in from the cosmos. Was Einstein right? Are there really
black holes? When two of these monsters swallow each other,
does it create a tidal wave of gravity detectable on our tiny
planet thousands or millions of light years away? Please
place your bets now.